Tachyonic chaos and causality in the open universe

Einstein coefficients and equilibrium formalism for tachyon radiation

“…is by deÿnition positive. As Lorentz boosts mix transversal and longitudinal components, a universal reference frame is not only necessary for the causality interpretation of superluminal signals [18,19,21,26], but also to unambiguously deÿne a positive energy for transversal and longitudinal tachyons. We specify the current in (2.1) by assuming that subluminal particles are coupled to the tachyonic vector potential in the same way as electric charges to the electromagnetic ÿeld, the electric charge being replaced by a tachyonic charge.…”

“…Refs. [3][4][5][6][7][8][9][10] and [11][12][13][14][15][16][17][18][19][20][21][22] for related discussions on causality, relativity, and synchronicity in few-body and statistical systems.…”

Tachyons, Lamb shifts and superluminal chaos

“…Whatever the speed of the tachyon, its world-line gets dense in the chaotic nucleus in the limits τ → 0, ∞, provided the initial or terminal point of the covering trajectory lies in the limit set, so that it intersects infinitely many lattice cells. If the expansion factor has turning or inflection points, a tachyonic worldline can even get dense in the chaotic nucleus within a finite time [9]. Another startling feature of tachyons, caused by the space expansion but independent of the topology of the 3-space, are mirror images; a tachyon may appear simultaneously at different locations in the geodesic rest frame of a uniformly moving observer [35].…”

“…The 3-space must be open, multiply connected, and hyperbolic (of constant negative curvature) [5]. Hyperbolicity is needed to generate the instability of geodesics [6][7][8], and the infinite volume and a multiply connected topology are necessary to allow evolution by global metrical deformations; a pictorial description of such deformations can be found in [9]. Finally, the multiply connected topology confines certain unstable world-lines to a finite region, the center of the open 3-space [5,10,11], so that they can get chaotic there, cf.…”

“…Concepts like mixing and ergodicity do not reflect the time evolution, since they are based on the geometric shapes of geodesics of infinite length. The mixing in the center tends to create a uniform distribution, but inhomogeneities will always remain in a finite time [9]. The evolution of the global topological structure of the 3-space can get visible in the angular anisotropy of the temperature of the cosmic microwave background radiation [12].…”